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Model problems from nonlinear elasticity: partial regularity results
Published online by Cambridge University Press: 14 February 2007
Abstract
In this paper we prove that every weak
and strong local
minimizer $u\in{W^{1,2}(\Omega,\mathbb{R}^3)}$ of the functional
$I(u)=\int_\Omega|Du|^2+f({\rm Adj}Du)+g({\rm det}Du),$
where $ u:\Omega\subset\mathbb{R}^3\to \mathbb{R}^3$
,
f grows like $|{\rm Adj}Du|^p$
, g grows
like $|{\rm det}Du|^q$
and
1<q<p<2, is $C^{1,\alpha}$
on an open
subset $\Omega_0$
of Ω such that
${\it meas}(\Omega\setminus \Omega_0)=0$
. Such
functionals naturally arise from nonlinear elasticity problems. The key
point in order to obtain the partial regularity result is to
establish an energy estimate of Caccioppoli type, which is based on
an appropriate choice of the test functions. The limit case
$p=q\le 2$
is also treated for weak local minimizers.
- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 1 , January 2007 , pp. 120 - 134
- Copyright
- © EDP Sciences, SMAI, 2007
References
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